Math Problem of the Day

The legendary Indian national hero Sid has many magical powers. For example, he can shoot lazer beams from his right eye. He can fly at 100 MPH, but that’s boring. He is also very skilled at writing poems. Sid uses his magical powers to create the Button thAt creaTes Many Arachnid moNsters (BATMAN). When the BATMAN is pressed,$$0.2x\cdot (\sin(2\pi \cdot x)+0.2x^2+1.2)$$ spiders are created, where x is the time since the last button press in minutes (or 0 if the button has never been pressed). Seungln is locked in a room with the BATMAN. Sreenath presses the button at time 0 and he will press it again one hour later. Seungln is allowed to press the button up to three times. Help Seungln minimize the number of spiders created.